How to find the velocity of the protons and antiprotons?

[yy205001]

Homework Statement

Some particle accelerators allow protons (p+) and antiprotons (p-) to circulate at equal speeds in opposite directions in a device called a storage ring. The particle beams cross each other at various points to cause p+ + p- collisions. In one collision, the outcome is p+ + p- yields e+ + e- + γ + γ, where γ represents a high energy gamma-ray photon. The electron and position are ejected from the collision at 0.9999995c and the gamma-ray photon wavelengths are found to be 1.0 X 10-6 nm. What were the proton and antiproton speeds prior to the collision?

m(e-)=9.11e-31(kg), λ(γ)=1e-6(nm)

Homework Equations

Ei = Ef
E=mc^2 - 0.5mu^2
E=γmc^2

The Attempt at a Solution

I have no ideas how to start and where to start in this question. Please help.

 

[tiny-tim]

hi yy205001!

(try using the X² button just above the Reply box )

conservation of energy?

 

[yy205001]

i don't know what does'' p+ + p- yields e+ + e- + γ + γ'' tell me?

 

[tiny-tim]

well, you know the mass of everything, and you know the wavelength of the photons, and the speed of the electrons

 

[yy205001]

but how can we get the mass of the gamma ray?

 

[tiny-tim]

the gamma ray is a photon, with zero mass

 

[yy205001]

oh! thank you=]